Colonel Mustard in the Aviary with the Candlestick: a limit cycle attractor transitions to a stable focus via supercritical Andronov-Hopf bifurcation

Abstract

We establish the means by which Mr. Boddy came to transition from a stable trajectory within the global phase space of Philadelphia, Pennsylvania to a stable point on the cement floor of an aviary near the west bank of the Schuylkill River. There exist no documented murder motives, and so the dynamical interaction leading to the crime must be reconstructed from circumstantial data. Our investigation proceeds in two stages. First we take an audio stream recorded within the aviary near the time of death to identify the local embedding dimension, thereby enumerating the suspects. Second, we characterize Mr. Boddy's pre- and post-mortem behavior in the phase space in terms of an attractor that undergoes an abrupt change in stability. A supercritical Andronov-Hopf bifurcation can explain this transition. Then we uniquely identify the murderer. Finally, we note long-term plans to construct an underlying dynamical model capable of predicting the stability of equilibria in different parameter regimes, in the event that Mr. Boddy is ever murdered again.